This is quite out of date information, but anyway -
We visited Prague in 2008. Nothing particularly stood out in terms of the coffee, but my favourite cafe by far was
http://www.uzelenehocaje.cz/
It's on the hill up to the Castle, and is a lovely little tea shop. It serves coffee, as well as mulled wine and mulled mead (and of course is open into the evening - that area of the town is relatively quiet in the evening btw), but it's main strength is teas - it has a huge range of green, white and black teas.
It was a fairly late discovery on our visit, but definitely one I recommend to others - it's just a lovely place. I vaguely remember the turkish coffee I had as being okay, and the green tea as fairly good, but the stand out memory is sat with a bowl of mulled mead, reading a book, after dinner.
3 Cup Chemex, Hario Syphon, French Press, 5 Ibrik, Stove Top/Moka Pot, Pour Over, Hario V60, Kalita Wave, Kantans, AeroPress, Vario Grinder, Porlex hand grinder, Turkish Hand Grinder, Turkish Hand Grinder Missing Handle